Question: The grades on a math midterm at Gardner Bullis are normally distributed with $\mu = 76$ and $\sigma = 2.5$. Jessica earned a $77$ on the exam. Find the z-score for Jessica's exam grade. Round to two decimal places.
Answer: A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Jessica's exam grade by subtracting the mean $(\mu)$ from her grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{77 - {76}}{{2.5}}} $ ${ z \approx 0.40}$ The z-score is $0.40$. In other words, Jessica's score was $0.40$ standard deviations above the mean.